I don't see any advantage of introducing f(x), so it doesn't appear in my work. Also, each line above is an equation that flows logically from the equation in the preceding line. When you have a line that represents only the derivative of one side of the equation, you lose the flow in the logic.

thanks for replying, it's always useful to see faster methods of reaching the solution. On the grading scheme we're given when our work is handed back, there is a section commenting on how much time our method would cost us in an exam.

I agree with you that I can't see the advantage of saying y = f(x), but this is what is done in my maths text book.

Staff: Mentor

I agree with you that I can't see the advantage of saying y = f(x), but this is what is done in my maths text book.

If the function is defined as f(x) = <whatever> then it makes sense, but if you're given an equation that involves only x and y, then it doesn't make sense to me to bring in f(x). In any case, y is not a function of x in this problem - for each x value other than -1/2 there are two y values.

That was kind of a minor point, though. What I think is more important is doing your work so that it flows logically.